Crystal (software)

CRYSTAL is a quantum chemistry ab initio program, designed primarily for calculations on crystals (3 dimensions), slabs (2 dimensions) and polymers (1 dimension) using translational symmetry, but it can also be used for single molecules.^[1] It is written by V.R. Saunders, R. Dovesi, C. Roetti, R. Orlando, C.M. Zicovich-Wilson, N.M. Harrison, K. Doll, B. Civalleri, I.J. Bush, Ph. D’Arco, and M. Llunell from Theoretical Chemistry Group at the University of Torino and the Computational Materials Science Group at the Daresbury Laboratory near Warrington in Cheshire, England. The current version is CRYSTAL14, released in June 2014. Earlier versions were CRYSTAL88, CRYSTAL92, CRYSTAL95, CRYSTAL98, CRYSTAL03, CRYSTAL06, and CRYSTAL09.

Features

Hamiltonians

• Hartree–Fock theory
  • Restricted
  • Unrestricted
• Density functional theory
  • Local functionals [L] and gradient-corrected functionals [G]

1. Exchange functionals
   1. Slater (LDA) [L]
   2. von Barth-Hedin (VBH) [L]
   3. Becke '88 (BECKE) [G]
   4. Perdew-Wang '91 (PWGGA) [G]
   5. Perdew-Burke-Ernzerhof (PBE) [G]
   6. Revised PBE functional for solids (PBEsol) [G]
   7. Second-order expansion GGA for solids (SOGGA) [G]
   8. Wu-Cohen '06 (WCGGA) [G]
2. Correlation functionals
   1. VWN (#5 parameterization) (VWN) [L]
   2. Perdew-Wang '91 (PWLSD) [L]
   3. Perdew-Zunger '81 (PZ) [L]
   4. von Barth-Hedin (VBH) [L]
   5. Lee-Yang-Parr (LYP) [G]
   6. Perdew '86 (P86) [G]
   7. Perdew-Wang '91 (PWGGA) [G]
   8. Perdew-Burke-Ernzerhof (PBE) [G]
   9. Revised PBE functional for solids (PBEsol) [G]
   10. Wilson-Levy '90 (WL) [G]
3. Hybrid HF-DFT functionals
   1. B3PW, B3LYP (using the VWN5 functional)
   2. User-defined hybrid functionals
4. Numerical-grid based numerical quadrature scheme
5. London-type empirical correction for dispersion interactions (Grimme scheme)

Energy derivatives

• Analytical first derivatives with respect to the nuclear coordinates and cell parameters
  • Hartree–Fock and density functional methods
  • All-electron and Effective Core Potentials

Types of calculation

• Single-point energy calculation
• Automated geometry optimization
  • Uses a modified conjugate gradient algorithm
  • Optimizes in symmetry-adapted cartesian coordinates
  • Optimizes in redundant coordinates
  • Full geometry optimization (cell parameters and atom coordinates)
  • Freezes atoms during optimization
  • Constant volume or pressure constrained geometry optimization (3D only)
  • Transition state search
• Harmonic vibrational frequencies
  • Harmonic frequencies at Gamma
  • Phonon dispersion using a direct approach (efficient supercell scheme)
  • IR intensities through either localized Wannier functions or Berry phase
  • Calculation of the reflectance spectrum
  • Exploration of the energy and geometry along selected normal modes
• Anharmonic frequencies for X-H bonds
• Automated calculation of the elastic tensor of crystalline systems (3D only)
• Automated E vs V calculation for equation of state (3D only)
• Automatic treatment of solid solutions

Basis set

• Gaussian type functions basis sets

1. s, p, d, and f GTFs
2. Standard Pople Basis Sets

• STO-nG n=2-6 (H-Xe), 3-21G (H-Xe), 6-21G (H-Ar)
• polarization and diffuse function extensions
• User-specified basis sets supported
• Pseudopotential Basis Sets
  • Hay-Wadt large core
  • Hay-Wadt small core
• User-defined pseudopotential basis sets supported

Periodic systems

• Periodicity
  • Consistent treatment of all periodic systems
  • 3D - Crystalline solids (230 space groups)
  • 2D - Films and surfaces (80 layer groups)
  • 1D - Polymers, space group derived symmetry (75 rod groups) and helical symmetry (up to order 48)
  • 0D - Molecules (32 point groups)
• Automated geometry editing
  • 3D to 2D - slab parallel to a selected crystalline face (hkl)
  • 3D to 0D - cluster from a perfect crystal (H saturated)
  • 3D to 0D - extraction of molecules from a molecular crystal
  • 3D to n3D - supercell creation
  • 2D to 1D - building nanotubes from a single-layer slab model
  • Several geometry manipulations (reduction of symmetry; insertion, displacement, substitution, deletion of atoms)

Wave function analysis and properties

• Band structure
• Density of states
  • Band projected DOSS
  • AO projected DOSS
• All Electron Charge Density - Spin Density
  • Density maps
  • Mulliken population analysis
  • Density analytical derivatives
• Atomic multipoles
• Electric field
• Electric field gradient
• Structure factors
• Compton profiles
• Electron Momentum Density
• Electrostatic potential and its derivatives
  • Quantum and classical electrostatic potential and its derivatives
  • Electrostatic potential maps
• Fermi contact
• Localized Wannier Functions (Boys method)
• Dielectric properties
  • Spontaneous polarization (Berry Phase)
  • Spontaneous polarization (Localized Wannier Functions)
  • Dielectric constant: new Coupled Perturbed HF(KS) scheme and Finite-field approximation

Software performance

• Memory management: dynamic allocation
• Full parallelization of the code
  • parallel SCF and gradients for both HF and DFT methods
  • Replicated data version (MPI)
  • Massive parallel version (MPI) (distributed memory)

Program structure

The program is built of two modules: crystal and properties. The crystal program is dedicated to perform the SCF calculations, the geometry optimizations, and the frequency calculations for the structures given in input. At the end of the SCF process, the program crystal writes information on the crystalline system and its wave function as unformatted sequential data in Fortran unit 9, and as formatted data in Fortran unit 98. One-electron properties and wave function analysis can be computed from the SCF wave function by running the program properties.

The main advantage of the crystal code is due to the deep and optimized exploitation of symmetry, at all levels of calculation (SCF as well gradients and vibrational frequencies calculations). This allows significant reduction of the computational cost for periodic calculations. Note that while the symmetry generally reduces to identity in large molecules, large crystalline system usually show many symmetry operators.

Theoretical background

The Hartree–Fock method for periodic systems

C. Pisani and R. Dovesi Exact exchange Hartree–Fock calculations for periodic systems. I. Illustration of the method. Int. J. Quantum Chem. 17, 501 (1980).

V.R. Saunders Ab Initio Hartree–Fock Calculations for periodic systems. Faraday Symp. Chem. Soc. 19, 79-84 (1984).

C.Pisani, R.Dovesi and C.Roetti Hartree–Fock ab-initio of crystalline systems, Lecture Notes in Chemistry, Vol. 48, Spinger Verlag, Heidelberg, 1988

The Coulomb problem

R. Dovesi, C. Pisani, C. Roetti and V.R. Saunders Treatment of Coulomb interactions in Hartree–Fock calculations of periodic systems. Phys. Rev. B28, 5781-5792, 1983

V. R. Saunders, C. Freyria Fava, R. Dovesi, L. Salasco and C. Roetti On the electrostatic potential in crystalline systems where the charge density is expanded in Gaussian Functions Molecular Physics, 77, 629-665, 1992

V. R. Saunders, C. Freyria Fava, R. Dovesi and C. Roetti On the electrostatic potential in linear periodic polymers. Computer Physics Communications, 84, 156-172, 1994

The exchange problem

M.Causa`, R. Dovesi, R. Orlando, C. Pisani and V. R.Saunders Treatment of the exchange interactions in Hartree–Fock LCAO calculation of periodic systems. J. Phys. Chem, 92, 909, 1988

The symmetry

R. Dovesi On the role of symmetry in the ab initio Hartree–Fock linear combination of atomic orbitals treatment of periodic systems. Int. J. Quantum Chem. 29, 1755 (1986).

C. Zicovich-Wilson and R. Dovesi On the use of Symmetry Adapted Crystalline Orbitals in SCF-LCAO periodic calculations. I. The construction of the Symmetrized Orbitals. Int. J. Quantum Chem. 67, 299-309 (1998).

C. Zicovich-Wilson and R. Dovesi On the use of Symmetry Adapted Crystalline Orbitals in SCF-LCAO periodic calculations. II. Implementation of the Self-Consistent-Field scheme and examples. Int. J. Quantum Chem. 67, 309-320 (1998).

DFT implementation

M.Causa`, R.Dovesi, C.Pisani, R.Colle and A.Fortunelli Correlation correction to the Hartree–Fock total energy of solids. Phys. Rev., B 36, 891, 1987

M.D. Towler, M. Causa' and A. Zupan Density functional Theory in periodic systems using local gaussian basis sets. Comp. Phys. Comm. 98, 181 (1996)

Analytical gradients implementation

K. Doll, V. R. Saunders, N. M. Harrison Analytical Hartree–Fock gradients for periodic systems. Int. J. Quantum Chem. 82, 1-13 (2001)

K. Doll, R. Dovesi, R. Orlando Analytical Hartree–Fock gradients with respect to the cell parameter for systems periodic in three dimensions. Theor. Chem. Acc. 112, 394-402 (2004).

Geometry Optimization

B. Civalleri, Ph. D'Arco, R. Orlando, V.R. Saunders, R. Dovesi Hartree–Fock geometry optimisation of periodic systems with the CRYSTAL code. Chem. Phys. Lett. 348, 131-138 (2001)

Localized Wannier Functions

C. M. Zicovich-Wilson, R. Dovesi and V. R. Saunders A general method to obtain well localized Wannier functions for composite energy bands in LCAO periodic calculations. J. Chem. Phys. 115, 9708-9718 (2001).

Vibration frequencies at Gamma

F. Pascale, C. M. Zicovich-Wilson, F. Lopez Gejo, B. Civalleri, R. Orlando, R. Dovesi The calculation of vibrational frequencies of crystalline compounds and its implementation in the CRYSTAL code J. Comput. Chem. 25, 888-897 (2004).

C. M. Zicovich-Wilson, F. Pascale, C. Roetti, V. R. Saunders, R. Orlando, R. Dovesi Calculation of vibration frequencies of alpha-quartz: the effect of hamiltonian and basis set. J. Comput. Chem.25, 1873–1881 (2004).

Calculation of dielectric constant

C. Darrigan, M. Rerat, G. Mallia, R. Dovesi Implementation of the finite field perturbation method in the CRYSTAL program for calculating the dielectric constant of periodic systems. J. Comp. Chem. 24, 1305–1312 (2003).

Calculation of properties of crystalline materials

C. Pisani Quantum-Mechanical Ab-initio calculation of the Properties of Crystalline Materials, Lecture Notes in Chemistry, Vol. 67, Spinger Verlag, Heidelberg, 1996

See also

• Crystal structure
• Quantum chemistry programs

References

1. Computational Chemistry, David Young, Wiley-Interscience, 2001. Appendix A. A.2.2 pg 334, Crystal

External links

• CRYSTAL
• Computational Materials Science Group
• Theoretical Chemistry Group University of Torino